When a liquid jet encounters a surface, it is spread out radially. Due to mass conservation the stream changes from a supercritical flow to a subcritical flow at a certain radius. This radius remains constant when the volumetric flow also remains constant. This Phenomenon known as hydraulic jump can easily be observed in a kitchen sink. My question is: when a circular container (e. g. a bucket or bottle) is filled up with e. g. water, at first a hydraulic jump appears. But as the water level rises there is more water around the hydraulic jump, flowing in the direction of the supercritical zone. Therefore the radius of the hydraulic jump decreases over time. My question is: When given certain parameters such as volumetric flow rate and container radius, is it possible to predict the time when the radius of the hydraulic jump equals zero?
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